Results 191 to 200 of about 6,252 (234)

Computing with Expansions in Gegenbauer Polynomials

SIAM Journal of Scientific Computing, 2009
We develop fast algorithms for computations involving finite expansions in Gegenbauer polynomials. A method is described to convert any finite expansion between different families of Gegenbauer polynomials. For a degree-$n$ expansion the computational cost is $\mathcal{O}(n(\log(1/\varepsilon)+|\alpha-\beta|))$, where $\varepsilon$ is the prescribed ...
exaly   +2 more sources

The expansion in Gegenbauer polynomials: A simple method for the fast computation of the Gegenbauer coefficients

Journal of Computational Physics, 2013
We present a simple and fast algorithm for the computation of the Gegenbauer transform, which is known to be very useful in the development of spectral methods for the numerical solution of ordinary and partial differential equations of physical interest.
Enrico de Micheli
exaly   +3 more sources

Adomian decomposition method by Gegenbauer and Jacobi polynomials

International Journal of Computer Mathematics, 2011
In this paper, orthogonal polynomials on [–1,1] interval are used to modify the Adomian decomposition method (ADM). Gegenbauer and Jacobi polynomials are employed to improve the ADM and compared with the method of using Chebyshev and Legendre polynomials.
Yücel Cenesiz
exaly   +3 more sources

An integral formula for generalized Gegenbauer polynomials and Jacobi polynomials

Advances in Applied Mathematics, 2002
In this interesting paper the author studies generalized Gegenbauer polynomials that are orthogonal with respect to the weight function \(|x|^{2\mu}\) \((1-x^2)^{\lambda- {1\over 2}}\). First, an important integral formula is established for these polynomials that serves as a transformation between \(h\)-harmonics of different parameters and contains ...
exaly   +2 more sources

Derivatives of Generalized Gegenbauer Polynomials

Theoretical and Mathematical Physics, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
García Fuertes, W., Perelomov, A. M.
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Gegenbauer Polynomials Revisited

The Fibonacci Quarterly, 1985
Der Gegenstand dieser Arbeit sind spezielle Polynome, die sich in der Tafel der Gegenbauerschen Polynome entlang der abnehmenden Diagonalen bilden. Dabei werden einige Eigenschaften dieser Polynome diskutiert wie z.B. expliziter Ausdruck, erzeugende Funktion, rekurrenter Ausdruck, Differentialgleichung u.s.w.
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On the Behavior of Gegenbauer Polynomials in the Complex Plane

Results in Mathematics, 2012
A real entire function \(f\) is said to be in the the Laguerre-Pólya class, denoted by \(\mathcal L\)-\(\mathcal P\), if \(f\) is the uniform limit, on compact subsets of \(\mathbb C\), of polynomials all of whose zeros are real. If \(f\in \mathcal L\text{-}\mathcal P\), then it is known that \[ |f(x+iy)|^2=\sum_{k=0}^{\infty} L_k(f; x)y^{2k},\quad x ...
Nikolov, Geno, Alexandrov, Alexander
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Higher Spin Generalisation of the Gegenbauer Polynomials

Complex Analysis and Operator Theory, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
David Eelbode, Tim Janssens
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Appendix: Gegenbauer Polynomials

2016
This chapter collects some properties of the Gegenbauer polynomials that we use throughout this work, in particular, in the proof of the explicit formulae for differential symmetry breaking operators (Theorems 1.5, 1.6, 1.7, and 1.8) and the factorization identities for special parameters (Theorems 13.1, 13.2, and 13.3).
Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner   +2 more
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The relativistic Hermite polynomial is a Gegenbauer polynomial

Journal of Mathematical Physics, 1994
It is shown that the polynomials introduced recently by Aldaya, Bisquert, and Navarro-Salas [Phys. Lett. A 156, 381 (1991)] in connection with a relativistic generalization of the quantum harmonic oscillator can be expressed in terms of Gegenbauer polynomials. This fact is useful in the investigation of the properties of the corresponding wave function.
openaire   +1 more source